2x5th-17x4th+33x3rd+23x2nd-59x-30

2x^{5}-17x^{4}+33x^{3}+23x^{2}-59x-30

See this link: https://www.askmehelpdesk.com/math-sciences/5th-degree-polynomial-coordinates-make-graph-332062.html

You can graph it to find the roots or use the Rational Root Theorem as I explained in the link provided. I would suggest googling the Rational Root Theorem or finding it in any algebra text.

The possible roots are factors of -30 and 2. The constant and leading coefficient.

Possible roots:

Choices for the numerator c: \pm 30, \;\ \pm 15, \;\ \pm 10, \;\ \pm 6 \;\ \pm 5, \;\ \pm 3 \;\ \pm 2, \;\ \pm 1

Choices for the denominator d: \pm 1 \;\ \pm 2

Choices for c/d, which I will not list. You can see those from the other two lists.

Try dividing the poly by one of the choices, say, 2. Divide it by x-2, if it reduces to a fourth power poly, then that is a root. Continue on.
This one is nice because it has 5 real roots.